1. Field of the Invention
The present invention relates to a method of detecting an image by using an imaging optical system such as a microscope, a camera, and an endoscope, and an apparatus which detects an image by using an imaging optical system such as a microscope, a camera, and an endoscope.
2. Description of the Related Art
In recent years, resolution of an image detecting apparatus in which an imaging optical system such as a microscope, a camera, and an endoscope is used has been improved. Particularly, in a field of microscopes and optical recording, an almost no aberration optical system has been realized, and a resolution as an imaging optical system has been constrained mainly by a diffraction limit of a visible light. On the other hand, as it has been disclosed in the following Non-Patent Literatures, an optical material in which a refractive index takes a negative value (hereinafter, called appropriately as “negative refraction material”) has been realized. It has been proposed that when the negative refraction material is used, it is possible to form an image having a very high resolution beyond the diffraction limit (hereinafter, called appropriately as “perfect imaging”).
As it has been disclosed in Non-Patent Literature Physical Review Letters, Volume 85, Page 3966 (2000), by J. B. Pendry, even in a case other than a case in which the refractive index takes a negative value, when a real part of a dielectric constant or a magnetic permeability is a negative value, for electromagnetic waves of a specific polarization state, the negative refraction phenomenon is observed. Moreover, as it has been disclosed in Non-Patent Literature Physical Review B, Volume 62, Page 10696 (2000), by M. Notomi, in a periodic structure such as a photonic crystal, as a result of a photonic band being turned up in a reciprocal lattice space, irrespective of being a material having each of the refractive index, the dielectric constant, and the magnetic permeability a positive value, a negative refraction phenomenon has been observed for electromagnetic waves of a specific wavelength and a specific polarization state.
In view of the abovementioned circumstances, in this specification, a material which exhibits a negative refraction response for specific electromagnetic waves is called as a “material exhibiting negative refraction”. It is needless to mention that an expression “material exhibiting negative refraction” is a concept having a wide sense than the negative refraction material.
Apart from the photonic crystals mentioned above, materials such as metallic thin films, chiral substances, photonic crystals, metamaterials, left-handed materials, backward wave materials, and negative phase velocity media have been known as the materials exhibiting negative refraction.
According to Non-Patent Literature Soviet Physics USPEKHI, Volume 10, Page 509 (1968), by V. G. Velelago et al., for a material having a negative value for both the dielectric constant and the magnetic permeability, the refractive index is also a negative value. Furthermore, it has been shown that such materials satisfy sort of like extension of Snell's law, which will be described later.
FIG. 9 shows a refraction of light in a general optical material (hereinafter, called appropriately as a “general optical material”) having a positive refractive index. When light is propagated from a medium 1 to a medium 2, the light is refracted at an interface of the two media. In this case, the Snell's law indicated by the following equation (1) is satisfied.n1 sin θ1=n1 sin θ2  equation (1)
Here, θ1 denotes an angle of incidence, θ2 denotes an angle of refraction, n1 denotes a refractive index of the medium 1, and n2 denotes a refractive index of the medium 2.
FIG. 10 shows a refraction of light when the refractive index n2 of the medium 2 takes a negative value. As shown in FIG. 10, light which is incident is refracted in a direction opposite to a direction of refraction shown in FIG. 9, with respect to a normal of the interface. In this case, when the angle of refraction θ2 is let to be a negative value, the equation satisfies the Snell's law mentioned above.
FIG. 11 shows an image forming relationship by a convex lens 13 in which a general optical material is used. Light from an object point 11A on an object plane 11 is focused at an image point 12A on an image plane 12. When the refractive index of the lens is positive, it is necessary that a lens surface has a finite curvature for image forming.
Whereas, a flat plate made of a material exhibiting negative refraction (hereinafter, called appropriately as “negative refraction lens”) can focus the light irrespective of the curvature being infinite. FIG. 12 shows an image formation relationship by a negative refraction lens 14. Light from an object point 11B on the object plane 11 is focused at an image point 12B on the image plane 12.
In an image forming optical system such as a microscope, an upper limit value of a theoretical resolution is determined by a diffraction limit. As it has been described in a textbook of optics such as Non-Patent Literature “Optics”, 4th edition (Addison-Wesley, Reading, Mass., 2002) by E. Hecht, according to Rayleigh criterion, a minimum distance between two resolvable points is λ/NA. Here, λ is a wavelength, and NA is the numerical aperture. Moreover, a structure smaller than the diffraction limit can not be resolved by an optical system.
Moreover, a microscope and an optical pickup which improve the resolution by using an objective lens such as a liquid-immersion objective lens, an oil-immersion objective lens, and a solid immersion objective lens, has been proposed. An effective NA is increased in these. Accordingly, a value of λ/NA equivalent to the diffraction limit is reduced. Here, the numerical aperture NA cannot be greater than a refractive index of a medium in which the object plane is disposed. Therefore, an upper limit for the numerical aperture NA is about 1.5 to 2.0.
Light which is emitted from the object point 11A on the object plane 11 forms two types of light waves namely propagating light which reaches up to a far distance and evanescent waves which are attenuated at a distance of about a wavelength from the object point 11A. The propagating light corresponds to a low-frequency component out of information on the object plane 11. The evanescent waves on the other hand, correspond to a high-frequency component out of the information on the object plane 11.
A boundary between the propagating light and the evanescent waves is a spatial frequency equivalent to 1/λ. Particularly, a spatial frequency in the object plane of the evanescent waves is higher than 1/λ. Therefore, a wave number component of the evanescent waves in a direction of propagation of light perpendicular to the object plane is an imaginary number. Therefore, the evanescent waves are attenuated rapidly as they are receded from the object plane 11.
Regarding the propagating light on the other hand, not all the components are advanced to an optical system. A part of the propagating light is eclipsed by an aperture in the optical system. Therefore, only a component of the spatial frequency on the object plane 11, which is smaller than NA/λ reaches the image plane 12. Ultimately, from information which reaches the image point 12A, the high-frequency component out of the information held by the object point 11A is missing. Accordingly, there is a spread of a point image due to diffraction, and the resolution is constrained.
In Non-Patent Literature Physical Review Letters, Volume 85, Page 3966 (2000)), by J. B. Pendry, which was disclosed in recent years, an amplification of the evanescent waves mentioned above in the negative refraction material has been disclosed. Therefore, it is shown that, in the image formation by the negative refraction lens 14 shown in FIG. 12, the amplitude of the evanescent waves on the image plane 12 is restored to the same quantity as on the object plane 11. In other words, in an optical system shown in FIG. 12, both the propagating light and the evanescent waves are transferred from the object plane 11 to the image plane 12. Therefore, information of the object point 11B is reproduced perfectly at the image point 12B. This means that when an image forming optical system in which the negative refraction lens 14 is used, the perfect imaging in which the resolution is not limited by the diffraction limit, is possible.
The perfect imaging mentioned above is not true only in theoretical terms. A negative refraction lens has been made, and results of experiments have been reported. For example, in Non-Patent Literature Physical Review Letters, Volume 84, Page 4184 (2000)), by D. R. Smith et al., a metamaterial in which a rod and a coil made of a metal, smaller than the wavelength are arranged periodically, has been made. Functioning of such metamaterial as a negative refraction lens in a microwave region has been reported.
Moreover, in Non-Patent Literature Physical Review B, Volume 62, Page 10696 (2000)), by M. Notomi, a method of making a negative refraction material by using a photonic crystal has been disclosed. In a photonic crystal in which air rods are arranged in a hexagonal lattice form, in a dielectric substance, a photonic band in which an effective refractive index is isotropic and negative exists. Furthermore, it is possible to consider the photonic crystal as a two-dimensional homogeneous negative refraction material with respect to electromagnetic waves in a frequency band which is accommodated in the photonic band.
For the perfect imaging by the negative refraction lens, there is a theoretical counterargument in a Non-Patent Literature Physical Review Letters, Volume 88, Page 187401 (2002)), by P. M. Valanju et al., which has lead to a controversy. However, in recent years, a theory of the negative refraction lens disclosed in Non-Patent Literature Physical Review Letters, Volume 85, Page 3966 (2000) by J. B. Pendry, has been generally accepted.
In an optical system in which a general optical material is used, it is possible to make an aplanatic point, in other words, a point at which a spherical aberration and a coma aberration become zero simultaneously. An image formed by this optical system invariably becomes an imaginary image. Therefore, when the negative refraction material is used, it is possible to form a real image by disposing an object plane at the aplanatic point (refer to Non-Patent Literature Physical review E, Volume 70, page 065601 (2004) by D. Schurig et al.). Thus, by using the negative refraction material, it is possible to perform a unique optical designing which has not been there so far.
Moreover, it has been known that for many metals, a real part of a dielectric constant for (with respect to) a visible light becomes negative. For example, according to Non-Patent Literature “Handbook of Advanced Optical Technologies” by J. Tsujiuchi et al., (published by Asakura Shoten, Japan 2002), silver exhibits a negative dielectric constant for light of a wavelength in a range of 330 nm to 900 nm. Furthermore, according to Non-Patent Literature, Science, Volume 306, Page 1353 (2004), by J. B. Pendry even in a chiral substance having a helical structure, there exists a photonic band exhibiting a negative refraction.
A phenomenon of negative refraction has unique characteristics differing from characteristics of a general optical material, such as having a negative angle of refraction, having a phase velocity and a group velocity in opposite directions, and that an electric field, a magnetic field, and a pointing vector form a left hand system in this order.
A name of a material which exhibits negative refraction has not yet been established in general. Therefore, under the characteristics mentioned above, such materials are sometimes called as “negative phase velocity materials”, “left handed materials”, “backward wave materials”, and “negative refraction materials”. In this specification, such material is treated as a type of a material which exhibits negative refraction. Such treatment is not at all contradictory considering a definition of the material exhibiting negative refraction.
Moreover, there are many phenomenon names which overlap with a name under (of) a material or a structure. For example, a metamaterials made of a metal resonator array are sometimes called as left-handed substances or left-handed metamaterials. These are also let to be included in the materials exhibiting negative refraction.
Thus, when a negative refraction lens formed by a negative refraction material is used, it is possible to realize an image forming optical system of a very high resolution (perfect imaging) in which the diffraction limit is not constrained (refer to Non-Patent Literature Physical Review Letters, Volume 85, Page 3966 (2000) by J. B. Pendry, for example). Furthermore, even in a case of image formation of only the propagating light, it is possible to have a unique optical designing (refer to Non-Patent Literature Physical Review E, Volume 70, Page 065601 (2004) by D. Schurig et al., for example).
However, for realizing the perfect imaging by the negative refraction lens, an absolute value of the refractive index of the negative refraction lens and an absolute value of a refractive index of a medium in which an object plane (image plane) is disposed have to be the exactly the same. When the absolute values of the refractive index differ slightly, or when there is a slight imaginary component in the refractive index of the negative refraction lens, the restoring of the evanescent waves is inhibited, and the image formation efficiency is declined.
According to Non-Patent Literature Applied Physical Letters, Volume 82, Page 1506 (2003) by D. R. Smith et al. for example, a resolution of the refraction lens having a refractive index −1.0+0.001i disposed in air (refractive index=1) is about twelve times of the diffraction limit. Moreover, when the refractive index of the negative refraction lens is −1.1+0.001i, evanescent waves up to about eight times of the diffraction limit, reach an image plane. However, evanescent waves of which frequencies are slightly higher than the evanescent waves up to about twelve times or eight times of the diffraction limit, are amplified resonantly. Due to such resonant enhancement, a favorable image formation performance cannot be achieved.
Next, a transfer function which is an index showing a resolution of an optical system will be described below. An amplitude distribution of light on an object plane is expressed by the following equation (2). An intensity distribution of light on the object plane is expressed by the following equation (3).A(x)=A0 cos(kx)  equation (2)I(x)=A02 cos2(kx)=(A02/2){1+cos(kx/2)}  equation (3)
Here, A denotes an amplitude on the object plane                A0 denotes a maximum amplitude on the object plane        k denotes a wave number        A′ denotes an amplitude on an image plane        A′0 denotes a maximum amplitude on the image plane        
An object which has the abovementioned amplitude and the intensity distribution is formed as an image (subjected to image formation) by a predetermined optical system. At this time, an amplitude distribution and an intensity distribution on the image plane are expressed by the following equation (ξ) and equation (5) respectively. Here, β is a lateral magnification of the optical system.A′(x)=A′0 cos(βkx)  equation (4)I′(x)=A′02 cos2(kx)=(A′02/2){βkx/2)}  equation (5)
In a real optical system, equation (4) and equation (5) take different function form due to an effect of scattering and interference of light. In this case, the intensity distribution which is observed actually may be subjected to Fourier transform, and a component of a spatial frequency βk may be extracted. A ratio of amplitudes A′0/A0 and a ratio of intensities A′02/A02 obtained in such manner are let to be called as an amplitude transfer function and an intensity transfer function respectively.
In a case when it is not necessary to distinguish the amplitude and the intensity, the two ratios mentioned above are called only as a transfer function. Moreover, in this specification, calling as “transfer function”, it includes both the amplitude transfer function and the intensity transfer function.
Thus, a transfer function which is peculiar to the optical system is called only as “transfer function”. Furthermore, a transfer function upon being subjected to compensating calculation process which will be described later is called as “compensated transfer function (transfer function compensation)”. Such a “compensated transfer function” is a concept of calculation processing, and is a state in which a characteristic curve of an original transfer function of the optical system is not changed by the calculation processing, and is in an original state.
When the transfer function (frequency dependence) in an image forming optical system in general is measured, the transfer function is declined rapidly near a spatial frequency equivalent to a resolution limit. Therefore, a structure which is smaller than the spatial frequency equivalent to the resolution limit cannot be resolved.
Moreover, in optical systems including an optical element which is formed by a material exhibiting negative refraction, since the resonant enhancement of the evanescent waves described above inhibits an image formation of a low frequency component carried by the propagating light, in addition to the smaller structure than the spatial frequency equivalent to the resolution limit, it is all the more damaging.